Determination of the Defining Boundary in Nuclear Magnetic Resonance Diffusion Experiments

Abstract

While nuclear magnetic resonance diffusion experiments are widely used to resolve structures confining the diffusion process, it has been elusive whether they can exactly reveal these structures. This question is closely related to x-ray scattering and to Kac's "hear the drum" problem. Although the shape of the drum is not "hearable," we show that the confining boundary of closed pores can indeed be detected using modified Stejskal-Tanner magnetic field gradients that preserve the phase information and enable imaging of the average pore in a porous medium with a largely increased signal-to-noise ratio.

Axon Diameters and Myelin Content Modulate Microscopic Fractional Anisotropy at Short Diffusion Times in Fixed Rat Spinal Cord

“…In the short mixing time regime, interesting diffusion-diffraction phenomena can be produced [32][33][34][35][36], and angular dependencies can provide insight into pore sizes as shown experimentally first by Koch and Finsterbusch [37,38] and then by others [39][40][41]; however, by analyzing the displacement correlation tensor [42], the short τ m angular DDE experiment aiming to measure compartment sizes was found by Jespersen to be equivalent to a time-dependent SDE experiment [43]. By contrast, in the long mixing time regime, the second order term in the displacement correlation tensor, from which sizes are measured, is decoupled from µA, making its measurement much less complicated [25,31].…”

Magnetic Resonance Pore Imaging: Overcoming the resolution limit of MRI for closed pore systems

“…1, the molecules will have visited all points inside the pore equally often. Therefore, the time averaged position of each molecule can be approximated to be in the center of mass of the pore space r cm [4]. Thus one arrives at Eðq; 1Þ ¼ expfi2pq Á r cm g S 0 ðqÞ ð 5Þ and, with the above stated limits, the ''long-narrow'' experiment returns the structure factor S 0 ðqÞ directly.…”

“…In this work we followed the approach of Laun et al where one of the gradients in the standard PGSE NMR experiment is reduced in amplitude and dramatically increased in duration, while the second gradient pulse has to be short and intense [4]. Because of this distinct gradient pattern this experiment has been dubbed ''long-narrow'' PGSE NMR [8].…”

“…Similar to other diffraction techniques, PGSE NMR shares the drawback of only measuring the square modulus of the structure factor in which the structural information is obscured due to the lack of phase information. A general approach suggested by Laun et al predicts that a modification of a single PGSE-NMR experiment would allow to acquire structure factors for arbitrary geometries [4]. Shemesh et al, on the other hand, introduced a synergistic approach using two PGSE NMR experiments [5] which has been shown to yield the structure factor for point symmetric pores [6,7].…”

Pulsed second order fields for parallel acquisition of q-space

“…Measurement of the diffusive process yields information about a range of properties, including the average propagator for displacement [1,2], the pore space geometry of porous media [3][4][5][6][7][8][9][10][11][12][13], and the characterisation of emulsions [14,15]. Measurement of this process using nuclear magnetic resonance was first described by Hahn [16], with further development and implementation using constant time and pulsed gradient fields by others [17][18][19][20].…”